**Graphs of functions.**
If we know the graph of ,
we can sketch the graphs of
,
, etc.

Equation of | Effect on the graph of |

Shift it vertically upward if , or downward if . | |

Shift it horizontally to the left if , or to the right if . | |

Stretch it vertically if , or compress it vertically if . | |

Stretch it horizontally if , or compress it horizontally if . |

Department of Mathematics